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General Relativity and Quantum Cosmology

Title:
Ringholes and closed timelike curves

Abstract: It is shown that in a classical spacetime with multiply connected space
slices having the topology of a torus, closed timelike curves are also formed.
We call these spacetime ringholes. Two regions on the torus surface can be
distinguished which are separated by angular horizons. On one of such regions
(that which surrounds the maximum circumference of the torus) everything
happens like in spherical wormholes, but the other region (the rest of the
torus surface), while still possessing a chronology horizon and non-chronal
region, behaves like a coverging, rather than diverging, lens and corresponds
to an energy density which is always positive for large speeds at or near the
throat. It is speculated that a ringhole could be converted into a time machine
to perform time travels by an observer who would never encounter any matter
that violates the classical averaged weak energy condition. Based on a
calculation of vacuum fluctuations, it is also seen that the angular horizons
can prevent the emergence of quantum instabilities near the throat.